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Artemon [7]
3 years ago
9

Solve the system of equations by substitution. x + y = A system of equations. StartFraction 3 over 8 EndFraction x plus StartFra

ction one-third EndFraction y equals StartFractions 17 over 24 EndFraction. x + 7y = 8 ( , )
Mathematics
2 answers:
Diano4ka-milaya [45]3 years ago
8 0

Answer:

x=1 and y=1

Step-by-step explanation:

We have to solve by substitution the given system of equations:

\left \{ {{\frac{3}{8}x+\frac{1}{3}y=\frac{17}{24} }\atop {x+7y=8}} \right.

First, we have to choose an equation, no matter which one, and isolate a certain variable, no matter which one either. So, by our own criteria, we choose the second equation, and we'll isolate <em>x</em>:

x+7y=8\\x=8-7y

Now, this equivalence for x, we will replace it in the other equation, instead of <em>x</em>, we will put the result:

\frac{3}{8}(8-7y)+\frac{1}{3}y=\frac{17}{24}

Then, we solve for <em>y</em>:

\frac{3}{8}(8-7y)+\frac{1}{3}y=\frac{17}{24}\\\frac{3}{8}8-\frac{3}{8}7y+\frac{1}{3}y=\frac{17}{24}\\-\frac{21}{8}y+\frac{1}{3}y=\frac{17}{24}-3\\\frac{-63y+8y}{24}=\frac{17-72}{24}\\ \frac{-55y}{24}=\frac{-55}{24}\\y=\frac{-55(24)}{24(-55)}=1

Now, the final process will be to replace this y<em>-value </em>in one equation, no matter which one, and find x<em>-value</em>:

x+7y=8\\\\x+7(1)=8\\x=8-7\\x=1

Therefore, the solution of the system is x=1 and y=1

Akimi4 [234]3 years ago
7 0

Answer:

<h2>(1,1)</h2>

Step-by-step explanation:

juss took it

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75

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Step-by-step explanation:

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7 0
2 years ago
An article describes a study comparing two methods of measuring mean arterial blood pressure. The auscultatory method is based o
zzz [600]

Answer:

p_v =P(t_{(5)}>0.499) =0.319

The p value is higher than any significance level given for example \alpha=0.05,0.1, so then we can conclude that we FAIL to reject the null hypothesis. So we don't have enough evidence to conclude that the mean reading is greater for the auscultatory method at 5% or 10% of significance.

Step-by-step explanation:

A paired t-test is used to compare two population means where you have two samples in  which observations in one sample can be paired with observations in the other sample. For example  if we have Before-and-after observations we can use it.  

Let put some notation  

x=Auscultatory method , y = Oscillatory method

x: 74 86 84 79 70 78 79 70

y: 70 85 90 110 71 80 69 74

The system of hypothesis for this case are:

Null hypothesis: \mu_x- \mu_y \leq 0

Alternative hypothesis: \mu_x -\mu_y >0

The first step is define the difference d_i=x_i-y_i, that is given so we have:

d: 6.6, 4.2, -5.5, -3.1, 9.3, -3.9

The second step is calculate the mean difference  

\bar d= \frac{\sum_{i=1}^n d_i}{n}=1.267

The third step would be calculate the standard deviation for the differences, and we got:

s_d =\sqrt{\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1}} =6.215

The fourth step is calculate the statistic given by :

t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{1.267 -0}{\frac{6.215}{\sqrt{6}}}=0.499

The next step is calculate the degrees of freedom given by:

df=n-1=6-1=5

Now we can calculate the p value, since we have a right tailed test the p value is given by:

p_v =P(t_{(5)}>0.499) =0.319

The p value is higher than any significance level given for example \alpha=0.05,0.1, so then we can conclude that we FAIL to reject the null hypothesis. So we don't have enough evidence to conclude that the mean reading is greater for the auscultatory method at 5% or 10% of significance.

5 0
2 years ago
What is the value of the fourth term in a geometric sequence for which a1= 30 and r = 1/2
Viktor [21]

Answer:

a_{4} = 3.75

Step-by-step explanation:

The n th term of a geometric sequence is

a_{n} = a₁(r)^{n-1}

where a₁ is the first term and r the common ratio

Here a₁ = 30 and r = \frac{1}{2}, thus

a_{4} = 30(\frac{1}{2}) ^{3} = 30 × \frac{1}{8} = \frac{30}{8} = \frac{15}{4} = 3.75

4 0
3 years ago
So i have 136 sq units in surface area of a rectangle how do i get 136 <br> plz helps as so you can
Savatey [412]

Answer:

well you answered the question in your question: you have Area = 136 square units. How you got it, you need to be more specific. Maybe it's because the side lengths are 2 * 68 for example. If anything provide more info. tried to help the best I can

Step-by-step explanation:

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3 years ago
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AURORKA [14]
A 6 down, A 6 right

hope this helped :)
6 0
3 years ago
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